Exponential improvements for superball packing upper bounds (Q2308311)

The authors show for every \(p \ge 2\) that the density of any packing of translates of the \(l_p\)-ball \(\mathbf{B}_p^n=\{(x_1,\ldots,x_n): |x_1|^p+\dots+|x_n|^p \le 1\}\) in \(\mathbb{R}^n\) does not exceed \(2^{(\gamma_p+o(1))n}\) with some \(\gamma_p < -1/p\) where \(n \to \infty\), this way improving a bound by \textit{J. G. van der Corput} and \textit{G. Schaake} [Acta Arith. 2, 152--160 (1936; Zbl 0015.15401)]. They give also upper bounds for \(1 \le p < 2\).